The not-for-profit compostable bags cost 5p, the same price as the conventional single-use plastic bags they will replace.
The scheme will start at Co-op stores in areas where the bags are accepted by the local authority in food waste collections.
The retail chain, which has 350 stores in Scotland and 2,600 UK-wide, says after shoppers use the bags to carry purchases home the bags can be used as bin liners and then turned into peat-free compost along with the household food waste.
The bags are approved for home composting.
However, the bags are not available in Scotmid stores.
The move is part of the Co-op’s ethical strategy “The Future of Food” which sets out how it will tackle issues such as plastic pollution, food waste, healthy eating, saving energy and trading fairly.
It is estimated that the new bags will remove around 60 million single-use plastic bags.
The scheme will be launched in 22 of the 32 council areas in Scotland.
Iain Ferguson, the Co-op’s environment manager, said: “Our members and customers expect us to help them to make more ethical choices, and we are dedicated to doing just that.
“Reducing environmental impacts is, and always has been, at the core of the Co-op’s efforts.
“The bags are carefully designed to help local authorities with food waste recycling, supporting their community and resident engagement and reducing plastic contamination in a targeted way.”
Mr Ferguson added: “We are working to get closer to what our members want, need and care about.
“We have committed to removing own-brand plastic products, and the launch of compostable carrier bags in our stores provides an environmentally friendly alternative to single-use plastic shopping bags.”
All major UK retailers have pledged to make 100 per cent of plastic packaging recyclable, re-useable or compostable by 2025.